Swarm-like earthquake sequences are commonly observed in a diverse range of geological settings including volcanic and geothermal regions as well as along transform plate boundaries. They typically lack a clear mainshock, cover an unusually large spatial area relative to their total seismic moment release, and fail to decay in time according to standard aftershock scaling laws. Swarms often result from a clear driving phenomenon, such as a magma intrusion, but most lack the necessary geophysical data to constrain their driving process. To identify the mechanisms that cause swarms on strike-slip faults, we use relative earthquake locations to quantify the spatial and temporal characteristics of swarms along Southern California and East Pacific Rise transform faults. Swarms in these regions exhibit distinctive characteristics, including a relatively narrow range of hypocentral migration velocities, on the order of a kilometre per hour. This rate corresponds to the rupture propagation velocity of shallow creep transients that are sometimes observed geodetically in conjunction with swarms, and is significantly faster than the earthquake migration rates typically associated with fluid diffusion. The uniformity of migration rates and low effective stress drops observed here suggest that shallow aseismic creep transients are the primary process driving swarms on strike-slip faults. Moreover, the migration rates are consistent with laboratory values of the rate-state friction parameter b (0.01) as long as the Salton Trough faults fail under hydrostatic conditions.